TECHNICAL FIELD

The invention relates to a method for improving heuristic algorithms used in optimization analyses of retaining walls in terms of reaching a solution faster.

PRIOR ART

Obtaining safe designs of geotechnical engineering structures using traditional methods requires repeating analyses and controls through making a large number of pre-sizing systematically. It is important that the designs carried out for the planning and construction of commonly encountered geotechnical engineering structures are economical as well as providing the stability conditions. Furthermore, the completion of the design process as soon as possible and the safe solution obtained being the most economical design among all possible solutions are other design criteria that should be considered. Carrying out comprehensive design studies that will take all the parameters and dimensions that affect the result using traditional methods into account is almost impossible in terms of time and cost.

Today, new methods such as optimization techniques are needed in obtaining the most economical design in a short time among the safe designs found as a result of all the trials carried out taking into account the complex structure of the problem with multiple variables under consideration. The software generally used for geotechnical engineering applications does not include optimization techniques developed for different disciplines recently. For such techniques to be able to be applied, there is a need to conduct further scientific research and to establish design criteria for optimum sizing of geotechnical structures.

Heuristic optimization methods are algorithms that produce solutions to large- scale optimization problems by making use of the solutions produced by nature in the face of difficult problems based on the laws of science, by being inspired by the nature, and by simulating the social behaviour of swarms. Heuristic methods can be considered in six different groups as biology-based, physics-based, swarm-based, social-based, music-based and chemistry-based groups, and there are hybrid methods obtained by using these methods together. Although these methods do not guarantee the exact solution, they have the quality to converge to the global solution considerably.

In the current optimization analyses, the mathematical expressions of the optimization problem are defined as operations to the algorithm and the optimum result is reached by running the algorithm thousands of times. The shortness of the defined operations helps the algorithm that is run many times to give results in shorter time.

In the solution of complex engineering problems, heuristic optimization algorithms, which are simple, effective, and easy to implement and reach the result in an acceptable time frame, have become more popular due to their features such as the need for derivative information of traditional optimization methods and the necessity of the starting point. There are many studies in the literature for the optimum design of retaining walls using heuristic optimization techniques such as simulated annealing algorithm (Ceranic et al., 2001 ), particle swarm optimization algorithm (Ahmadi-Nedushan and Varaee, 2009), big bang-big crunch algorithm (Camp and Akin, 2012), firefly algorithm (Sheikholeslami et al., 2014), gravity search algorithm (Khajehzadeh & Eslami, 2012) and teaching-learning based algorithm (Temur & Bekda§, 2016). In the study conducted by Gandomi et al. (2015), the optimization results obtained using particle swarm optimization, firefly, and cuckoo algorithms, known as swarm intelligence algorithms, were compared with one another. Soil properties such as angle of internal friction, weight per unit of volume, pore water pressure, and geometric parameters of the wall cross-section affect the design of the retaining wall, which must provide stability conditions and must be economical. Parametric studies investigating the effect of such factors affecting the optimum retaining wall design were conducted by different researchers (Yepes et al. (2008) and Molina-Moreno et al. (2017)) and the effect of the variation of parameters on optimum designs were investigated.

Dagdeviren and Kaymak (2018) examined the parameters affecting the optimum cost design of reinforced concrete retaining walls. The optimum cost design of five hundred different retaining walls that meet the internal stability and structural stability criteria was investigated by using the artificial bee colony algorithm, taking into account different wall heights, surcharge load, filled soil internal friction angle and passive soil pressure coefficient values.

In another study, the optimum design of the reinforced concrete cantilever retaining wall was investigated using the harmony search algorithm and a cost design was made (Akin and Saka, 2010). In the reinforced concrete cantilever retaining wall, which is used most widely among reinforced concrete retaining structures, wall height, toe extension, upper and bottom stem thicknesses, foundation base width, foundation thickness, key height, key thickness, toe-key distance are used as design parameters.

BRIEF DESCRIPTION OF THE INVENTION

The invention relates to a method for improving heuristic algorithms used in optimization analyses of retaining walls in terms of reaching a solution faster. A method has been developed in which the safety factors of sliding, overturning, and slope stability of the retaining walls can be estimated according to the target value selected by the Taguchi method, which is used for statistical-based experimental design and quality improvement. The developed method has been used as a constraint and objective function in optimization analysis. Geotechnical engineering structures, design parameters, and design criteria used in the formation of the method presented within the scope of the patent are given in the chart (Chart 1 ).

Chart 1. Geotechnical engineering structures, design parameters and design criteria used LIST OF FIGURES

Figure 1. Harmony Search Algorithm Flow Chart

Figure2. Artificial Bee Colony Algorithm Flow Chart

Figures. Method Flow Chart

DETAILED DESCRIPTION OF THE INVENTION

Optimization in engineering is defined as making the necessary designs to manufacture or operate the most beneficial system at minimum cost or to achieve maximum gain or efficiency. Optimization methods are generally divided into two as deterministic and heuristic. Mathematical-based deterministic methods may be insufficient in cases such as the complex structure of the problem with many variables, infinite solution space, or the high number of iterations. It is very difficult to obtain optimum designs that take all the parameters that affect the behaviour of the system together into account with mathematical-based deterministic methods. Because, in the design and sizing of such structures, usually a system is selected and pre-sizing is done, and then necessary controls (investigations) and analyses are made for the selected dimensions. However, there are uncertainties about whether the selected system and dimensions are the optimum system or dimensions, and whether or not a more economical system or dimension than the chosen one exists etc. These situations have driven the heuristic optimization methods forward which have been used effectively and scientific studies on which have been made recently. Heuristic optimization methods are algorithms that produce solutions to large-scale optimization problems by making use of the solutions produced by nature in the face of difficult problems based on the laws of science, by being inspired by the nature, and by simulating the social behaviour of swarms.

Harmony search, which is developed by Geem et al. (2001 ), and is used in the invention, is based on the principle of finding the best harmony with notes played by the musicians in an orchestra (Fig. 1 ). The facts that in harmony algorithm, initial values are not needed, the global solution can be reached in multiple aspects without hanging up on the local solution, both separate and continuous variables are used in the optimization and iterations are completed in a short time make this method more advantageous compared to others.

Artificial bee colony algorithm, which is another algorithm used within the scope of the invention and developed by Karaboga (2005), is an algorithm that is inspired by the swarm intelligence that is effective between the interpersonal communication among the swarm and provides the basic life needs such as nutrition, defence and migration (Figure 2).

In the method to be protected, in order to obtain the optimum dimensions by taking into account the soil properties determined before the design of the retaining walls, the results obtained from the physical tests are subjected to a series of algorithm operations through the software in a device, and the optimum design that meets the stability criteria for different internal friction angle values of the soil and different wall heights is revealed. Here, the device can be a computer, mobile phone, tablet, or any hardware that can run the software.

The details of the method that is the subject to our invention will be given in this section.

- Before the design of the retaining wall, which is widely used in geotechnical engineering to meet the lateral ground pressures, soil investigations are carried out in the area to be built.

- Within the scope of these soil investigations, laboratory and field tests are applied to determine the physical properties of the soil (unit volume weight, internal friction angle, etc.), soil stratification status, groundwater level, etc. parameters.

- The soil profile and soil properties to be designed are obtained by performing tests such as Standard Penetration (SPT), Cone Penetration (CPT), Dilatometer (DMT), Pressuremeter (PMT) in the field. Among the mentioned field tests, SPT test is one of the oldest field tests, which is widely used in Turkey as well as in many countries of the world. The simplicity of the test set-up, it being low cost as it can be easily applied in the well drilled during the drilling process, the ability to take samples from the drilling pits, and the ability to be applied in all test groups and under the groundwater level are the superior aspects of the SPT test compared to other tests.

- Parameters required for foundation design, wall design, liquefaction analysis etc. can be obtained with various correlations by performing a Standard Penetration Test on the soil where a retaining wall is planned to be constructed. In this experiment, the basic principle is to obtain the total number of blows required for the hammer with a weight of 63.5 kilograms to be dropped from a height of 762 mm and the probe (split-barrel sampler) with the hardened steel tip to dip into the soil by 305 mm. The probe dips into the soil for a total of 45 cm, the first 15 cm is the disturbed part and is not taken into account. The number of blows recorded for the probe to penetrate the last 30cm into the soil is recorded as the SPT-N value. After the hammering is complete, the probe (split-barrel sampler) is removed from the borehole. The split sampler is opened, and a representative soil sample is taken. Identification tests such as sieve analysis and determination of consistency limits are performed on these samples brought to the laboratory environment.

- Undisturbed soil samples taken from the field during drilling are brought to the laboratory environment and subjected to tests such as free pressure, triaxial pressure, consolidation, etc. and mechanical parameters of the soil are determined.

- Depth (CN), energy (CE), drill rods (CR), borehole diameter (CB), sheath correction (Cs), hammer head (CA), ram pad (Cc), frequency of number of blowes (CBF) and groundwater level corrections are made on the SPT-Nfieid numbers obtained after the field test, and Neo and Ni.eo values are obtained (Sivrikaya and Togrol, 2009).

Here, Neo corresponds to the number of blows corrected according to 60% of the theoretical free fall ram energy and Ni.eo corresponds to 60% of the theoretical free fall ram energy and the number of blows corrected by taking the effective geological pressure of 100kPa.

- By using the corrected values of the SPT-N numbers obtained from the field, the internal friction angle (0,°) in the soil environment properties where the design of the retaining wall that is the subject of this patent application will be made is determined. In the literature, there are many correlations specified by different researchers given in Chart 2 below to obtain the 0 value by using the corrected SPT-N numbers (Sivrikaya and Togrol, 2009).

Chart 2. Correlations between SPT-N and 0 in the literature

The application steps of the method that is the subject of the invention are as follows: - Detailed soil examination, laboratory and field tests of the soil environment, and the construction site where the retaining wall will be designed are carried out.

- The internal friction angle (0, °) of the soil required for obtaining the optimum retaining wall design is determined by making use of the relationships given in the literature according to the Ni,eo value obtained by performing the Standard Penetration test performed in the field.

- The wall height (H), which is another necessary parameter for obtaining the optimum retaining wall design, is determined according to the coordinates determined for the construction area during the land survey and the land elevation data measured with devices such as digital level and total station. In addition, the presence of an adjacent structure or road, the foundation and basement level of the adjacent structure and similar factors are also factors that are effective in determining the height of the wall.

- In the first step of the optimization, constraints for H and 0 design parameters and objective function obtained from field and laboratory measurements for retaining wall design are entered into the software containing statistics-based developed mathematical models (the one amongst Formula flow - 1 , Formula flow - 2 or Formula flow - 3, which is suitable according to the type of bearing wall) that differ according to the type of retaining wall in the device, and the optimization algorithm is started.

- In the search for the optimum design of the retaining wall, a large design pool is created containing different and discrete values of the design variables. This design pool comprises wall dimensions such as foundation base length, toe extension, heel extension, base thickness, front face angle, base slope, and key height in order to obtain optimum dimensions of the retaining wall.

- As, in the search for the best solution, the combination that is the most optimal (with the minimum objective function value) among the randomly selected values from this design pool and also provides the stability criteria entered into the algorithm as limiting is assigned as the best solution, these values are put into their places together with the H and 0 design parameters assigned in the statistics-based mathematical model, and the safety factors of sliding, overturning and slope stability are determined.

- The heuristic optimization algorithm (Figure 1 and Figure 2) is run until the selected maximum number of iterations is reached, and the optimum solution (wall design) that meets the constraints is recorded.

- Since heuristic optimization algorithms search for the optimum solution randomly, it is possible to obtain different optimum solutions (designs) in each execution of the algorithms. For this reason, the algorithm, which is run for the maximum number of iterations, is run at least 30 more times independently of each other, and the optimum solutions (designs) obtained for each run are recorded. - Among the optimum solutions (designs) obtained as a result of all different runs, the solution with the best design (minimum objective function value) is recorded as the most optimal wall design.

Below are the mathematical models used in the software.

General representation of the mathematical model: